Bernie Ecclestone has been told he must make a better job of selling Formula One by leading figures hosting this Sunday’s US Grand Prix in Texas.

This week the sport travels to Austin in crisis, with the futures of Caterham and Marussia in the balance, and other teams close to the wall. Pressure is mounting on Ecclestone, the sport’s chief executive and commercial rights holder, to take note, with the message from Mario Andretti, the official ambassador for the race in Austin, and Bobby Epstein, the co-founder of the Circuit of the Americas (Cota), that F1 needs to “loosen up a bit” and “make the sport about personalities”.

Caterham went into administration on Friday and have been given special dispensation not to take part in the next two races as they seek a buyer. Marussia went into administration on Monday and will also miss the next two grands prix, though they are still planning to take part in the final race of the season, in Abu Dhabi on 23 November.

The next two most desperate teams are Sauber and Lotus, who in 2012 and 2013 posted respective losses of more than £22m and £64.9m. Williams, one of the most famous names in F1, who are running third in the constructors’ championship, have already reported a six months’ loss of £20m for 2014. Even the biggest teams have struggled to replace dwindling sponsorship in recent years.

F1 has had no coherent leadership in the past year while Ecclestone, who will be 84 on Tuesday, fought bribery allegations in London and Munich courts. Now, against a background of spiralling costs, unequal payments to teams, falling crowds and TV audiences, as well as declining sponsorship and no agreement about capping costs, the sport has reached the point of no return.

How apt, then, that Ecclestone – who continues to spin gold for shareholders, the private equity company CVC Capital, if not the teams – has been given a blueprint for the sport’s future by the best salesmen in the world, the Americans, who want a closer relationship between drivers and fans as well as greater use of social media.

Andretti, the Italian-American who won the world title in 1978, told the Guardian: “Formula One should loosen up a bit. I think they’ve gone slightly overboard with the technical side of the engine. And we saw in Sochi [the previous race in Russia], teams backing off for fuel reasons, just to make it to the end.

“I would love to see a team invite a third car for a special event. For the US Grand Prix, say, Mercedes could invite a third car, having groomed some well-known American driver in testing, to take part as a guest competitor. Can you imagine what that would do for the promotion of the event? Every newspaper in the country would write about it.”

He added: “There are ways of using a little bit of creativity to enhance and increase the interest. It’s all there for the taking. It’s just a question of looking at some of the stranger rules they have in F1. Some people might laugh at that, but what I’m saying is very valid. And as time goes by they may have to look at things like this. F1 should explore every angle.”

Epstein added: “F1 has got to make the sport about personalities. That’s what Nascar does very well. Formula One can learn a lot from Nascar, from Hollywood. People connect with people. They don’t connect with metal. I would encourage the teams to make a priority the accessibility that the fans have to the drivers.

“Look at Lewis Hamilton. F1 should get him out there as much as they can, because he’s a great driver and a very good ambassador. The more Mercedes let him step out and be himself, the better. He’s an incredibly marketable guy. FI could look at the model of [US] PGA golfers, who have got really close to their fans.”

Jason Dial, the president of Cota, also feels Formula One should make a greater effort to involve its fan base. “I’d like to see F1 taken off the track and be more about engagement. There is real upside in the brand really growing, in terms of accessibility and digital social engagement. I think these type of things could really move the needle. From a business standpoint I want to engage our fans, and I want to build the fan base. I want to make it younger. I want to grow the pie. That’s what I’m focusing on.

“From a product-offering standpoint, accessibility is something that really plays well in the US market. Fans love to be close to the drivers and the machines. This is incredible technology. It’s one of the sport’s core equities.

“People love watching from afar but if they can get up close, so much the better. We’ve experienced that here in other events.”

The message from Austin has already been delivered to Formula One by people and countries with greater experience in staging grands prix and it is felt by many observers that the sport’s failure to listen – Ecclestone has dismissed social media as little more than a fad – is the main reason why it is in such difficulty.

In Monaco last year Martin Whitmarsh, then McLaren’s team principal and chairman of the Formula One Teams’ Association, warned: “I fear that we will have a crisis and then we will have to get real and sort it out. I cannot see, in their shoes [the seven smaller teams], how you can construct a sustainable business model.”

At the same time Bob Fernley, Force India’s deputy team principal, told the Guardian that CVC had been “a disaster” for the sport. He said: “I think they have done an absolutely awful job. In my view they are the worst thing that has ever happened to Formula One. They have done nothing whatsoever for the sport.”

CVC has made an estimated $8.2bn from its investment in Formula One since 2006 but its profits have not been reinvested in the sport. Formula One itself is also culpable. The teams have gone their own selfish ways and their failure to manage the cost of the development and supply of this year’s engines has been a major factor in the crisis.

As Graeme Lowdon, the president of Marussia put it just days before his team joined Caterham in administration: “The current recipe, in terms of sporting and technical regulations, has produced a sport that nobody can afford.”